Question

A 27.4 kg dog is running northward at 2.19 m/s , while a 7.19 kg cat is running eastward at 2.78 m/s . Their 75.7 kg owner has the same momentum as the two pets taken together. Find the direction and magnitude of the owner's velocity.

Answer 1

Answer:

$\| \vec v\| = 0.836\,\frac{m}{s}$, $\alpha = 71.577^{\textdegree}$ (Northeast)

Explanation:

Let consider that owner has the resultant direction of the momentums from the dog and the cat. First, the momentum of the owner is:

$\|\vec p \| = \sqrt{\left[(27.4\,kg)\cdot \left(2.19\,\frac{m}{s} \right)\right]^{2}+\left[(7.19\,kg)\cdot \left(2.78\,\frac{m}{s} \right)\right]^{2}}$

$\|\vec p \| = 63.248\,kg\cdot \frac{m}{s}$

The speed of the owner is:

$\|\vec v \| = \frac{63.248\,kg\cdot \frac{m}{s}}{75.7\,kg}$

$\| \vec v\| = 0.836\,\frac{m}{s}$

Lastly, the direction of the owner is:

$\alpha = \tan^{-1}\left[\frac{(27.4\,kg)\cdot \left(2.19\,\frac{m}{s} \right)}{(7.19\,kg)\cdot \left(2.78\,\frac{m}{s} \right)} \right]$

$\alpha = 71.577^{\textdegree}$ (Northeast)